A unified spray model for engine spray simulation using dynamic mesh refinement

This study is based on dynamic mesh refinement and uses spray breakup models to simulate engine spray dynamics. It is known that the Lagrangian discrete particle technique for spray modeling is sensitive to gird resolution. An adequate spatial resolution in the spray region is necessary to account for the momentum and energy coupling between the gas and liquid phases. This study uses a dynamic mesh refinement algorithm that is adaptive to spray particles to increase the accuracy of spray modeling. On the other hand, the accurate prediction of the spray structure and drop vaporization requires accurate physical models to simulate fuel injection and spray breakup. The present primary jet breakup model predicts the initial breakup of the liquid jet due to the surface instability to generate droplets. A secondary breakup model is then responsible for further breakup of these droplets. The secondary breakup model considers the growth of the unstable waves that are formed on the droplet surface due to the aerodynamic force. The simulation results are compared with experimental data in gasoline spray structure and liquid penetration length. Validations are also performed by comparing the liquid length of a vaporizing diesel spray and its variations with different parameters including the orifice diameter, injection pressure, and ambient gas temperature and density. The model is also applied to simulate a direct-injection gasoline engine with a realistic geometry. The present spray model with dynamic mesh refinement algorithm is shown to predict the spray structure and liquid penetration accurately with reasonable computational cost.     

近场水下爆炸气泡脉动及水射流的实验与数值模拟研究

海上作战时,近场水下爆炸形成的水射流能造成水面舰船结构的严重局部毁伤。为了研究近场爆炸时舰船底部水射流的形成机理及规律,开展了TNT当量2.5 g的炸药在固支方板底部不同爆距下起爆的水下爆炸实验。结果表明,气泡坍塌形成水射流的过程随着爆距的增加由吸附式向非吸附式转化。接着,基于ABAQUS软件采用CEL方法开展了系列数值模拟,结果表明:爆距在0.821～0.867倍最大气泡半径时,存在吸附式射流向非吸附式射流转化的临界点;固支方板加快了气泡坍塌的进程,炸药与钢板间的距离越小则射流形成的时间越早;射流形成过程中最大速度和射流击中钢板时速度均随着爆距的增大先增大后减小,并在临界点附近达到最大值,射流速度最大可达621 m/s,射流击中钢板时速度最大可达269 m/s。最后,给出了射流开始形成时间、射流最大速度、射流最大速度出现时间、射流击中钢板速度和射流击中钢板时间与距离参数的函数关系式。     

Mean Flow and Turbulence Measurements in a Turbulent Free Cruciform Jet

The results of measurements of all three components of the mean velocity vector, the Reynolds normal and primary shear stresses and the mean static pressure in a turbulent free jet, issuing from a sharp-edged cruciform orifice, are presented in this paper. The measurements were made with an x-array hot-wire probe and a pitot-static tube in the near flow field of the jet. The Reynolds number, based upon the equivalent diameter of the orifice, was 1.70 × 10⁵. In addition to the quantities measured directly, the mean streamwise centreline velocity decay, the jet half-velocity widths, the jet spreading rate, the mean streamwise vorticity, the mass entrainment rate, the integral momentum flux and the one-dimensional energy spectra have been derived from the measured data. The results show that the mean streamwise centreline velocity decay rate of the cruciform jet is higher than that of a round jet issuing from an orifice with the same exit area as that of the cruciform orifice. The mean streamwise velocity field changed shape continuously from a cruciform close to the orifice exit plane to circular at 12 and half equivalent diameters downstream. The mean streamwise vorticity field, up to about three equivalent diameters downstream of the orifice exit plane, consists of four pairs of counter-rotating cells, which are aligned with the four edges in the centre of the cruciform orifice.     

Vortex ring modelling of toroidal bubbles

During the collapse of a bubble near a surface, a high-speed liquid jet often forms and subsequently impacts upon the opposite bubble surface. The jet impact transforms the originally singly-connected bubble to a toroidal bubble, and generates circulation in the flow around it. A toroidal bubble simulation is presented by introducing a vortex ring seeded inside the bubble torus to account for the circulation. The velocity potential is then decomposed into the potential of the vortex ring and a remnant potential. Because the remnant potential is continuous and satisfies the Laplace equation, it can be modelled by the boundary-integral method, and this circumvents an explicit domain cut and associated numerical treatment. The method is applied to study the collapse of gas bubbles in the vicinity of a rigid wall. Good agreement is found with the results of Best (J. Fluid Mech. 251 79–107, 1993), obtained by a domain cut method. Examination of the pressure impulse on the wall during jet impact indicates that the high-speed liquid jet has a significant potential for causing damage to a surface. There appears to be an optimal initial distance where the liquid jet is most damaging.     

Developing structure of two-phase flow in a large diameter pipe at low liquid flow rate

In order to develop the interfacial area transport equation for the interfacial transfer terms in the two-fluid model, accurate data sets on axial development of local parameters such as void fraction, interfacial area concentration, interfacial gas velocity and Sauter mean diameter are indispensable to verify the modeled source and sink terms in the interfacial area transport equation. From this point of view, local measurements of both group 1 spherical/distorted bubbles and group 2 cap/slug bubbles in vertical upward air–water two-phase flow in a large diameter pipe with 200 mm in inner diameter and 26 m in height were performed at three axial locations of z/D = 41.5, 82.8 and 113 as well as 11 radial locations from r/R = 0–0.95 by using four-sensor probe method. Here, z, r, D and R are the axial distance from the inlet, radial distance from the pipe center, pipe diameter and pipe radius, respectively. The liquid flow rate and the void fraction ranged from 0.0505 m/s to 0.312 m/s and from 1.98% to 32.6%, respectively in the present experiment. The flow condition covered extensive region of bubbly flow, cap turbulent flow as well as their transition. The extensive analysis on the radial profiles of local flow parameters and their axial developments demonstrate the development of interfacial structures along the flow direction due to the bubble coalescence and breakup and the gas expansion. The significant decrease in void faction and interfacial area concentration and the increase in Sauter mean diameter and interfacial velocity were observed when the gradual flow regime transition occurred. Finally, the net change in the interfacial area concentration due to the bubble coalescence and breakup was quantitatively investigated in the present paper to reflect the true transfer mechanisms in observed two-phase flows.     

Formation of the finely dispersed gas phase in upward and downward fluid flows

The influence of the fluid and gas flow rate parameters on the diameter of bubbles separating from a single capillary immersed in a fluid flow in a channel of 1×1 cm cross-section is investigated. The dependences of the mean bubble diameter on the fluid velocity and the gas flow rate through the capillary are obtained. The frequency of the bubble detachment from the capillary is estimated. It is shown that the histogram of the bubble size distribution changes qualitatively with the excess of a certain critical bubble detachment frequency, which is associated with the transition from the discrete to jet mode of detachment.     

Bubbly flow undergoing a steep pressure gradient

The effects of a steep pressure gradient on bubbly flow were studied to determine the cause of noise emanating from components of a piping system. We used an orifice to generate a local pressure difference. The behavior of bubbles passing through the orifice was observed by using a video camera, and the noise was measured by a condenser microphone outside the pipe. It was found that the sound pressure level of noise generated by a bubbly flow was proportional to the pressure difference. An empirical formula for estimating noise level is proposed. The changes in size and number of bubbles passing through an orifice were found related to the breakup, which is affected by pressure difference rather than airflow rate. The breakup of a single bubble undergoing a steep pressure difference was observed to determine the mechanism of sound generation. It was found that a bubble was broken by impingement of an inward protrusion in the bubble. The growth rate of the protrusion depended on the pressure difference.     

Flow regime transitions due to cavitation in the flow through an orifice

This paper presents both experimental and theoretical aspects of the flow regime transitions caused by cavitation when water is passing through an orifice. Cavitation inception marks the transition from single-phase to two-phase bubbly flow; choked cavitation marks the transition from two-phase bubbly flow to two-phase annular jet flow.

It has been found that the inception of cavitation does not necessarily require that the minimum static pressure at the vena contracta downstream of the orifice, be equal to the vapour pressure liquid. In fact, it is well above the vapour pressure at the point of inception. The cavitation number [σ = (P₃ − P_v)/(0.5 pV²); here P₃ is the downstream pressure, P_v is the vapour pressure of the liquid, ρ is the density of the liquid and V is the average liquid velocity at the orifice] at inception is independent of the liquid velocity but strongly dependent on the size of the geometry. Choked cavitation occurs when this minimum pressure approaches the vapour pressure. The cavitation number at the choked condition is a function of the ratio of the orifice diameter (d) to the pipe diameter (D) only. When super cavitation occurs, the dimensionless jet length [L/(D - d); where L is the dimensional length of the jet] can be correlated by using the cavitation number. The vaporization rate of the surface of the liquid jet in super cavitation has been evaluated based on the experiments.

Experiments have also been conducted in which air was deliberately introduced at the vena contracta to simulate the flow regime transition at choked cavitation. Correlations have been obtained to calculate the critical air flow rate required to cause the flow regime transition. By drawing an analogy with choked cavitation, where the air flow rate required to cause the transition is zero, the vapour and released gas flow rate can be predicted.     

PIV measurements of a turbulent jet issuing from round sharp-edged plate

An experimental investigation is presented of a turbulent jet issuing from a round sharp-edged orifice plate (OP) into effectively unbounded surroundings. Planar measurements of velocity were conducted using Particle Image Velocimetry (PIV) in the near and transition regions. The Reynolds number, based on the jet initial diameter and velocity, is approximately 72,000. The instantaneous and mean velocities, Reynolds normal and shear stresses were obtained. The centerline velocity decay and the half-velocity radius were derived from the mean velocity. It is revealed that primary coherent structures occur in the near field of the OP jet and that they are typically distributed asymmetrically with respect to the nozzle axis. Comparison of the present PIV and previous hot-wire measurements for the OP jet suggests that high initial turbulence intensity leads to reduced rates of decay and spread of the mean flow field and moreover a lower rate of variation of the turbulence intensity. Results also show that self-similarity of the mean flow is well established from the transition region while the turbulent statistics are far from self-similar within the measured range to 16 diameters.     

NUMERICAL ANALYSIS ON THE VELOCITY AND PRESSURE FIELDS INDUCED BYMULTI-OSCILLATIONS OF AN UNDERWATER EXPLOSION BUBBLE

假设水下爆炸气泡的内部气体在膨胀收缩过程中满足绝热条件,周围流体无黏无旋不可压缩. 基于势流理论,采用边界元法研究气泡动力学行为,重点关注气泡引起的流场脉动载荷以及滞后流特性,给出了相关的理论推导和数值计算方法. 通过将数值结果与解析解、实验值进行对比,数值模型的收敛性和有效性能够得到保证. 利用编写的程序进行计算和分析,发现在气泡加速膨胀阶段,流场压力在气泡径向不一定是逐渐衰减,还有可能以先增后减的规律变化;气泡射流后,为了能够继续描述环状气泡的运动以及流场特性,将此时的流场分为无旋场和一个布置在气泡内部涡环的叠加,计算过程中采用了一些数值技巧处理气泡的拓扑结构,得以连续模拟多个周期的气泡运动. 环状气泡具有相对较高的上浮迁移速度,而且在其顶部和底部附近分别形成两个高压区,顶部的高压区峰值相对较大,底部的高压区范围相对较大. 环状气泡中心轴上的流场速度会在气泡中心有一个加速过程,在气泡顶部附近又迅速减小.     

气泡多周期运动时引起的流场压力与速度

假设水下爆炸气泡的内部气体在膨胀收缩过程中满足绝热条件,周围流体无黏无旋不可压缩. 基于势流理论,采用边界元法研究气泡动力学行为,重点关注气泡引起的流场脉动载荷以及滞后流特性,给出了相关的理论推导和数值计算方法. 通过将数值结果与解析解、实验值进行对比,数值模型的收敛性和有效性能够得到保证. 利用编写的程序进行计算和分析,发现在气泡加速膨胀阶段,流场压力在气泡径向不一定是逐渐衰减,还有可能以先增后减的规律变化;气泡射流后,为了能够继续描述环状气泡的运动以及流场特性,将此时的流场分为无旋场和一个布置在气泡内部涡环的叠加,计算过程中采用了一些数值技巧处理气泡的拓扑结构,得以连续模拟多个周期的气泡运动. 环状气泡具有相对较高的上浮迁移速度,而且在其顶部和底部附近分别形成两个高压区,顶部的高压区峰值相对较大,底部的高压区范围相对较大. 环状气泡中心轴上的流场速度会在气泡中心有一个加速过程,在气泡顶部附近又迅速减小.      

Droplet size and velocity characteristics of water-air impinging jet atomizer

A water-air impinging jets atomizer is investigated in this study, which consists of flow visualization using high speed photography and mean droplet size and velocity distribution measurements of the spray using Phase Doppler Anemometry (PDA). Topological structures and break up details of the generated spray in the far and near fields are presented with and without air jet and for an impinging angle of 90°. Spray angle increases with the water jet velocity, air flow rate and impinging angle. PDA results indicate that droplet size is smallest in the spray center, with minimum value of Sauter mean diameter (SMD) of 50 µm at the air flow rate of Q_m = 13.50 g/min. SMD of droplets increases towards the spray outer region gradually to about 120 µm. The mean droplet velocity component W along the air-jet axis is highest in the spray center and decreases gradually with increasing distance from the spray center. SMD normalized by the air nozzle diameter is found firstly to decrease with gas-to-liquid mass ratio (GLR) and air-to-liquid momentum ratio (ALMR) and then remain almost constant. Its increasing with aerodynamic Weber number indicates an exponential variation. The study sheds light on the performance of water-air impinging jets atomizers providing useful information for future CFD simulation works.     

Measurements in the near flow field of an isosceles triangular turbulent free jet

The near field mean flow and turbulence characteristics of a turbulent jet of air issuing from a sharp-edged isosceles triangular orifice into still air surroundings have been examined experimentally using hot-wire anemometry and a pitot-static tube. For comparison, some measurements were made in an equilateral triangular free jet and in a round free air jet, both of which also issued from sharp-edged orifices. The Reynolds number, based on the orifice equivalent diameter, was 1.84×10⁵ in each jet. The three components of the mean velocity vector, the Reynolds normal and primary shear stresses, the one-dimensional energy spectra of the streamwise fluctuating velocity signals and the mean static pressure were measured. The mean streamwise vorticity, the half-velocity widths, the turbulence kinetic energy and the local shear in the mean streamwise velocity were obtained from the measured data. It was found that near field mixing in the equilateral triangular jet is faster than in the isosceles triangular and round jets. The mean streamwise vorticity field was found to be dominated by counter-rotating pairs of vortices, which influenced mixing and entrainment in the isosceles triangular jet. The one-dimensional energy spectra results indicated the presence of coherent structures in the near field of all three jets and that the equilateral triangular jet was more energetic than the isosceles triangular and round jets.     

Spray features in the near field of a flow-blurring injector investigated by high-speed visualization and time-resolved PIV

In a flow-blurring (FB) injector, atomizing air stagnates and bifurcates at the gap upstream of the injector orifice. A small portion of the air penetrates into the liquid supply line to create a turbulent two-phase flow. Pressure drop across the injector orifice causes air bubbles to expand and burst thereby disintegrating the surrounding liquid into a fine spray. In previous studies, we have demonstrated clean and stable combustion of alternative liquid fuels, such as biodiesel, straight vegetable oil and glycerol by using the FB injector without requiring fuel pre-processing or combustor hardware modification. In this study, high-speed visualization and time-resolved particle image velocimetry (PIV) techniques are employed to investigate the FB spray in the near field of the injector to delineate the underlying mechanisms of atomization. Experiments are performed using water as the liquid and air as the atomizing gas for air to liquid mass ratio of 2.0. Flow visualization at the injector exit focused on a field of view with physical dimensions of 2.3 mm × 1.4 mm at spatial resolution of 7.16 µm per pixel, exposure time of 1 µs, and image acquisition rate of 100 k frames per second. Image sequences illustrate mostly fine droplets indicating that the primary breakup by FB atomization likely occurs within the injector itself. A few larger droplets appearing mainly at the injector periphery undergo secondary breakup by Rayleigh–Taylor instabilities. Time-resolved PIV is applied to quantify the droplet dynamics in the injector near field. Plots of instantaneous, mean, and root-mean-square droplet velocities are presented to reveal the secondary breakup process. Results show that the secondary atomization to produce fine and stable spray is complete within a few diameters from the injector exit. These superior characteristics of the FB injector are attractive to achieve clean combustion of different fuels in practical systems.     

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

Large scale structure in gas-liquid mixture flows

Relatively slow variation in mixture void fraction in gas-liquid mixture flows are indicated by low pass filter averaging. The slow void fluctuations are found to have a regular characteristic frequency or scale in the churn flow regime or near the boundary with the dispersed bubble flow regime. These regular disturbances develop inherently in a vertical pipe flow in strength and in size and are not due to the method of flow mixing. There was no evidence of distinctive gas slugs in the flow, and the structures were identified as large clouds of bubbles which moved faster than the average velocity, growing in size and strength as they moved with the flow. The magnitude of the voidage fluctuations in the churn flow regime was on average 57% of the value for a slug flow. The large scale bubble clouds convect coherently over relatively long distances at up to 1.45 times the mean mixture flow velocity at a gas volume flow fraction of 0.4. In the bubble flow regime, the slow voidage variations were more random in scale and were only approx. 10% of the slug flow (maximum possible) value. However, even in the bubble flow regime, the disturbances convected coherently over relatively long distances at a velocity of approx. 1.1 times the mean mixture velocity.     

Modeling of bubble behaviors and size distribution in a slab continuous casting mold

Population balance equations combined with Eulerian–Eulerian two-phase model are employed to predict the polydispersed bubbly flow inside the slab continuous-casting mold. The class method, realized by the MUltiple-SIze- Group (MUSIG) model, alongside with suitable bubble breakage and coalescence kernels is adopted. A two-way momentum transfer mechanism model combines the bubble induced turbulence model and various interfacial forces including drag, lift, virtual mass, wall lubrication, and turbulent dispersion are incorporated in the model. A 1/4th scaled water model of the slab continuous-casting mold was built to measure and investigate the bubble behavior and size distribution. A high speed video system was used to visualize the bubble behavior, and a digital image processing technique was used to measure the mean bubble diameter along the width of the mold. Predictions by previous mono-size model and MUSIG model are compared and validated against experimental data obtained from the water model. Effects of the water flow rate and gas flow rate on the mean bubble size were also investigated. Close agreements by MUSIG model were achieved for the gas volume fraction, liquid flow pattern, bubble breakage and coalescence, and local bubble Sauter mean diameter against observations and measurements of water model experiments.     

Experimental investigation of horizontal air–water bubbly-to-plug and bubbly-to-slug transition flows in a 3.81 cm ID pipe

The present study seeks to investigate horizontal bubbly-to-plug and bubbly-to-slug transition flows. The two-phase flow structures and transition mechanisms in these transition flows are studied based on experimental database established using the local four-sensor conductivity probe in a 3.81 cm inner diameter pipe. While slug flow needs to be distinguished from plug flow due to the presence of large number of small bubbles (and thus, large interfacial area concentration), both differences and similarities are observed in the evolution of interfacial structures in bubbly-to-plug and bubbly-to-slug transitions. The bubbly-to-plug transition is studied by decreasing the liquid flow rate at a fixed gas flow rate. It is found that as the liquid flow rate is lowered, bubbles pack near the top wall of the pipe due to the diminished role of turbulent mixing. As the flow rate is lowered further, bubbles begin to coalesce and form the large bubbles characteristic of plug flow. Bubble size increases while bubble velocity decreases as liquid flow rate decreases, and the profile of the bubble velocity changes its shape due to the changing interfacial structure. The bubbly-to-slug transition is investigated by increasing the gas flow rate at a fixed liquid flow rate. In this transition, gas phase becomes more uniformly distributed throughout the cross-section due to the formation of large bubbles and the increasing bubble-induced turbulence. The size of small bubbles decreases while bubble velocity increases as gas flow rate increases. The distributions of bubble size and bubble velocity become more symmetric in this transition. While differences are observed in these two transitions, similarities are also noticed. As bubbly-to-plug or bubbly-to-slug transition occurs, the formation of large elongated bubbles is observed not in the uppermost region of bubble layer, but in a lower region. At the beginning of transitions, relative differences in phase velocities near the top of the pipe cross-section to those near the pipe center become larger for both gas and liquid phases, because more densely packed bubbles introduce more resistance to both phases.     

Analysis of the characteristic lengths in the bubble and slug flow regimes generated in a capillary T-junction

We present an analysis of the geometry of the continuous and disperse phases in the bubble and slug flow regimes in air–water mixtures generated in a capillary T-junction of 1  mm internal diameter. Bubble size dispersion is very low in the considered flow patterns. The concept of unit cell is used to identify two characteristic lengths of the two-phase flow, namely, the unit cell length and the bubble length. The relationship between these lengths and the gas and liquid superficial velocities, gas mean velocity, bubble generation frequency and volume average void fraction is analysed. We conclude that in the considered configuration the unit cell and bubble lengths can be predicted either by the ratio of the gas–liquid superficial velocities or the volume average void fraction.